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arXiv · 2212.04256

A new formula for intersection numbers

Bertrand Eynard·Dimitrios Mitsios
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Abstract

We propose a new formula to compute Witten--Kontsevich intersection numbers. It is a closed formula, not involving recursion neither solving equations. It only involves sums over partitions of products of factorials, double factorials and Kostka numbers (numbers of semi-standard tableau of given shape and weight) with bounded weights. As an application, we prove a conjecture of [ELO21] stating that the generating polynomials of the intersection numbers expressed in the basis of elementary symmetric polynomials have an unexpected vanishing of their coefficients.

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Bertrand Eynard, Dimitrios Mitsios. 2022-12-08. A new formula for intersection numbers. https://arxiv.org/abs/2212.04256

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